The phonon dispersion curves, the phonon DOS projected onto selected atoms, the Eliashberg function \(\alpha ^2F(\omega )\) , and the intergraded EPC constant \(\lambda (\omega )\)  were calculated as shown in Fig. 4(b). The absence of imaginary frequency along the high symmetry k path indicates the thermodynamic stability of Fmm-La\(_{0.5}\) Ce\(_{0.5}\) H\(_{10}\) . We note that the phonon spectrum can be divided into two regions. The lower branches with frequencies below 350 cm\(^{-1}\)  are mainly contributed to the motions of La and Ce atoms, in good agreement with the obtained Raman spectra [Fig. 3(b)]. The higher frequencies branches are dominated by hydrogen vibrations. An EPC parameter \(\lambda \)  of 2.69 is obtained from the combined contributions of \(\sim \)  28% and 72% for the low and high branches, respectively. The large EPC is derived from the high-frequency optical modes of hydrogen. Compared to the \(\lambda \)  value of 0.69 and 1.86 in fcc CeH\(_{10}\)  and LaH\(_{10}\)  at same conditions [1]}, [2]}, we find the strengthened EPC in La\(_{0.5}\) Ce\(_{0.5}\) H\(_{10}\)  owing to the replacement of La by Ce atoms, strongly supporting our motivation. Using the Eliashberg equation [3]}, we calculated \(T_c\)  of 164-182 K for La\(_{0.5}\) Ce\(_{0.5}\) H\(_{10}\)  by using the typical values of 0.10-0.13 for the Coulomb potential \(\mu ^\ast \) . The experimentally observed \(T_c\)  of 175\(\pm \) 2 K is well reproduced by the calculations, indicating that the electron-phonon interactions can account for the superconductivity of Fmm-La\(_{0.5}\) Ce\(_{0.5}\) H\(_{10}\) .
